Version 0.5, April 11, 2018

Jiri Spitz <jiri.spitz@bluetone.cz>

This module provides a feature complete GLPK interface for the Pure programming language, which lets you use all capabilities of the GNU Linear Programming Kit (GLPK) directly from Pure.

GLPK (see http://www.gnu.org/software/glpk) contains an efficient simplex LP solver, a simplex LP solver in exact arithmetics, an interior-point solver, a branch-and-cut solver for mixed integer programming and some specialized algorithms for net/grid problems. Using this interface you can build, modify and solve the problem, retrieve the solution, load and save the problem and solution data in standard formats and use any of advanced GLPK features.

The interface uses native Pure data types - lists and tuples - so that you need not perform any data conversions to/from GLPK internal data structures.

To make this module work, you must have a GLPK installation on your system, the version 4.42 or higher is required.

- Installation
- Error Handling
- Further Information and Examples
- Interface description
- Descriptions of interface functions
- Basic API routines
- Problem creating and modifying routines
- Create the GLPK problem object
- Set the problem name
- Set objective name
- Set the objective direction
- Add new rows to the problem
- Add new columns to the problem
- Set the row name
- Set the column name
- Set (change) row bounds
- Set (change) column bounds
- Set (change) objective coefficient or constant term
- Load or replace matrix row
- Load or replace matrix column
- Load or replace the whole problem matrix
- Check for duplicate elements in sparse matrix
- Sort elements of the constraint matrix
- Delete rows from the matrix
- Delete columns from the matrix
- Copy the whole content of the GLPK problem object to another one
- Erase all data from the GLPK problem object
- Delete the GLPK problem object

- Problem retrieving routines
- Get the problem name
- Get the objective name
- Get the objective direction
- Get number of rows
- Get number of columns
- Get name of a row
- Get name of a column
- Get row type
- Get row lower bound
- Get row upper bound
- Get column type
- Get column lower bound
- Get column upper bound
- Get objective coefficient
- Get number of nonzero coefficients
- Retrive a row from the problem matrix
- Retrive a column from the problem matrix

- Row and column searching routines
- Problem scaling routines
- LP basis constructing routines
- Simplex method routines
- Solve the LP problem using simplex method
- Solve the LP problem using simplex method in exact arithmetics
- Retrieve generic status of basic solution
- Retrieve generic status of primal solution
- Retrieve generic status of dual solution
- Retrieve value of the objective function
- Retrieve generic status of a row variable
- Retrieve row primal value
- Retrieve row dual value
- Retrieve generic status of a column variable
- Retrieve column primal value
- Retrieve column dual value
- Determine variable causing unboundedness

- Interior-point method routines
- Solve the LP problem using interior-point method
- Retrieve status of interior-point solution
- Retrieve the objective function value of interior-point solution
- Retrieve row primal value of interior-point solution
- Retrieve row dual value of interior-point solution
- Retrieve column primal value of interior-point solution
- Retrieve column dual value of interior-point solution

- Mixed integer programming routines
- Set column kind
- Retrieve column kind
- Retrieve number of integer columns
- Retrieve number of binary columns
- Solve the MIP problem using branch-and-cut method
- Retrieve status of mip solution
- Retrieve the objective function value of mip solution
- Retrieve row value of mip solution
- Retrieve column value of mip solution

- Additional routines

- Problem creating and modifying routines
- Utility API routines
- Problem data reading/writing routines
- Routines for MathProg models
- Problem solution reading/writing routines
- Write basic solution in printable format
- Read basic solution from a text file
- Write basic solution into a text file
- Print sensitivity analysis report
- Write interior-point solution in printable format
- Read interior-point solution from a text file
- Write interior-point solution into a text file
- Write MIP solution in printable format
- Read MIP solution from a text file
- Write MIP solution into a text file

- Advanced API routines
- LP basis routines
- Check whether basis factorization exists
- Compute the basis factorization
- Check whether basis factorization has been updated
- Get basis factorization parameters
- Change basis factorization parameters
- Retrieve the basis header information
- Retrieve row index in the basis header
- Retrieve column index in the basis header
- Perform forward transformation
- Perform backward transformation
- Warm up LP basis

- Simplex tableau routines

- LP basis routines
- Branch-and-cut API routines
- Basic routines
- Determine reason for calling the callback routine
- Access the problem object
- Determine additional row attributes
- Compute relative MIP gap
- Access application-specific data
- Select subproblem to continue the search
- Provide solution found by heuristic
- Check whether can branch upon specified variable
- Choose variable to branch upon
- Terminate the solution process

- The search tree exploring routines
- The cut pool routines

- Basic routines
- Graph and network API routines
- Miscellaneous routines

- Basic API routines

Get the latest source from https://bitbucket.org/purelang/pure-lang/downloads/pure-glpk-0.5.tar.gz.

Run `make` to compile the module and `make install` (as root) to install
it in the Pure library directory. This requires GNU make, and of course you
need to have Pure installed.

The default make options suppose that GLPK was configured with the following
options:
`--enable-dl --enable-odbc --enable-mysql --with-zlib --with-gmp`

The zlib library is a part of the GLPK source distribution from the
version 4.46 onwards, so the the configure options for newer GLPK versions are:
`--enable-dl --enable-odbc --enable-mysql --with-gmp`

Using the given options the depndencies are:

- GNU Multiprecision Library (GMP) - serves for the exact simplex solver. When disabled, the exact solver still works but it is much slower.
- ODBC library - serves for reading data directly from database tables within the GNU MathProg language translator through the ODBC interface.
- MySQL client library - serves for reading data directly from MySQL tables within the GNU MathProg language translator.
- zlib compression library - enables reading and writing gzip compressed problem and solution files.
- ltdl dlopen library - must be enabled together with any of ODBC or MySQL (or zlib for GLPK versions 4.45 and earlier).

`make` tries to guess your Pure installation directory and platform-specific
setup. If it gets this wrong, you can set some variables manually. In
particular, `make install prefix=/usr` sets the installation prefix, and
`make PIC=-fPIC` or some similar flag might be needed for compilation on 64
bit systems. The variable `ODBCLIB` specifies the ODBC library to be linked
with. The default value is `ODBCLIB=-lodbc`. Please see the Makefile for
details.

When an error condition occurs, the GLPK library itself prints an error mesage and terminates the application. This behaviour is not pleasant when working within an interpreter. Therefore, the Pure - GLPK bindings catches at least the most common errors like indices out of bounds. On such an error an appropriate message is returned to the interpreter. The less common errors are still trapped by the GLPK library.

When one of the most common errors occurs, an error term of the form
`glp::error message` will be returned, which specifies what kind of error
happend. For instance, an index out of boundsd will cause a report like the
following:

`glp::error "[Pure GLPK error] row index out of bounds"`

You can check for such return values and take some appropriate action. By
redefining `glp::error` accordingly, you can also have it generate exceptions
or print an error message. For instance:

`glp::error message = fprintf stderr "%s\n" message $$ ();`

**NOTE:** When redefining `glp::error` in this manner, you should be aware
that the return value of `glp::error` is what will be returned by the other
operations of this module in case of an error condition. These return values
are checked by other functions. Thus the return value should still indicate
that an error has happened, and not be something that might be interpreted
as a legal return value, such as an integer or a nonempty tuple. It is usually
safe to have `glp::error` return an empty tuple or throw an exception, but
other types of return values should be avoided.

**IMPORTANT:** It is really good to define a `glp::error` function,
otherwise the errors might remain unnoticed.

For further details about the operations provided by this module please see the GLPK Reference Manual. Sample scripts illustrating the usage of the module can be found in the examples directory.

Most GLPK functions and symbols live in the namespace `glp`. There are a few
functions and symbols in the namespace `lpx`. These functions and symbols
are likely to be removed and replaced by new ones in the future.

In general, when you replace the `glp_` prefix from the GLPK Reference Manual
with the namespace specification `glp::` then you receive the function name
in this module. The same is valid for `lpx_` and `lpx::`. The symbolic
constants are converted into lower case in this module, again obeying the
same prefix rules.

**Synopsis**:

```
glp::create_prob
```

**Parameters**:

none

**Returns**:

pointer to the LP problem object

**Example**:

```
> let lp = glp::create_prob;
> lp;
#<pointer 0x9de7168>
```

**Synopsis**:

```
glp::set_prob_name lp name
```

**Parameters**:

lp: pointer to the LP problem object name: problem name

**Returns**:

()

**Example**:

```
> glp::set_prob_name lp "Testing problem";
()
```

**Synopsis**:

```
glp::set_obj_name lp name
```

**Parameters**:

lp: pointer to the LP problem object name: objective name

**Returns**:

()

**Example**:

```
> glp::set_obj_name lp "Total costs";
()
```

**Synopsis**:

```
glp::set_obj_dir lp direction
```

**Parameters**:

lp: pointer to the LP problem object

direction: one of the following:

glp::min: minimize glp::max: maximize

**Returns**:

()

**Example**:

```
> glp::set_obj_dir lp glp::min;
()
```

**Synopsis**:

```
glp::add_rows lp count
```

**Parameters**:

lp: pointer to the LP problem object count: number of rows to add

**Returns**:

index of the first row added

**Example**:

```
> let first_added_row = glp_add_rows lp 3;
> first_added_row;
6
```

**Synopsis**:

```
glp::add_cols lp count
```

**Parameters**:

lp: pointer to the LP problem object count: number of columns to add

**Returns**:

index of the first column added

**Example**:

```
> let first_added_col = glp_add_cols lp 3;
> first_added_col;
5
```

**Synopsis**:

```
glp::set_row_name lp (rowindex, rowname)
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index rowname: row name

**Returns**:

()

**Example**:

```
> glp::set_row_name lp (3, "The third row");
()
```

**Synopsis**:

```
glp::set_col_name lp (colindex, colname)
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index colname: column name

**Returns**:

()

**Example**:

```
> glp::set_col_name lp (3, "The third column");
()
```

**Synopsis**:

```
glp::set_row_bnds lp (rowindex, rowtype, lowerbound, upperbound)
```

**Parameters**:

lp: pointer to the LP problem object

rowindex: row index

rowtype: one of the following:

glp::fr: free variable (both bounds are ignored) glp::lo: variable with lower bound (upper bound is ignored) glp::up: variable with upper bound (lower bound is ignored) glp::db: double bounded variable glp::fx: fixed variable (lower bound applies, upper bound is ignored) lowerbound: lower row bound

upperbound: upper row bound

**Returns**:`()`**Example**::`glp::set_row_bnds lp (3, glp::up, 0.0, 150.0);`

**Synopsis**:

```
glp::set_col_bnds lp (colindex, coltype, lowerbound, upperbound)
```

**Parameters**:

lp: pointer to the LP problem object

colindex: column index

coltype: one of the following:

glp::fr: free variable (both bounds are ignored) glp::lo: variable with lower bound (upper bound is ignored) glp::up: variable with upper bound (lower bound is ignored) glp::db: double bounded variable glp::fx: fixed variable (lower bound applies, upper bound is ignored) lowerbound: lower column bound

upperbound: upper column bound

**Returns**:

()

**Example**:

```
> glp::set_col_bnds lp (3, glp::db, 100.0, 150.0);
()
```

**Synopsis**:

```
glp::set_obj_coef lp (colindex, coefficient)
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index, zero index denotes the constant term (objective shift)

**Returns**:

()

**Example**:

```
> glp::set_obj_coef lp (3, 15.8);
()
```

**Synopsis**:

```
glp::set_mat_row lp (rowindex, rowvector)
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index rowvector: list of tuples (colindex, coefficient); only non-zero coefficients have to be specified, the order of column indices is not important, duplicates are notallowed

**Returns**:

()

**Example**:

```
> glp::set_mat_row lp (3, [(1, 3.0), (4, 5.2)]);
()
```

**Synopsis**:

```
glp::set_mat_col lp (colindex, colvector)
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index colvector: list of tuples (rowindex, coefficient); only non-zero coefficients have to be specified, the order of row indices is not important, duplicates are notallowed

**Returns**:

()

**Example**:

```
> glp::set_mat_col lp (2, [(4, 2.0), (2, 1.5)]);
()
```

**Synopsis**:

```
glp::load_matrix lp matrix
```

**Parameters**:

lp: pointer to the LP problem object matrix: list of tuples (rowindex, colindex, coefficient); only non-zero coefficients have to be specified, the order of indices is not important, duplicates are notallowed

**Returns**:

()

**Example**:

```
> glp::load_matrix lp [(1, 3, 5.0), (2, 2, 3.5), (3, 1, -2.0), (3, 2, 1.0)];
()
```

**Synopsis**:

```
glp::check_dup numrows numcols indices
```

**Parameters**:

numrows: number of rows numcols: number of columns indices: list of tuples (rowindex, colindex); indices of only non-zero coefficients have to be specified, the order of indices is not important

**Returns**:

returns one of the following:

0: the matrix has no duplicate elements -k: rowindex or colindex of the k-th element in indices is out of range +k: the k-th element in indices is duplicate

**Remark:**

Notice, thatkcounts from 1, whereas list members are counted from 0.

**Example**:

```
> glp::check_dup 3 3 [(1, 3), (2, 2), (3, 1), (2, 2)];
4
```

**Synopsis**:

```
glp::sort_matrix lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

()

**Example**:

```
> glp::sort_matrix lp;
()
```

**Synopsis**:

```
glp::del_rows lp rows
```

**Parameters**:

lp: pointer to the LP problem object rows: list of indices of rows to be deleted; the order of indices is not important, duplicates are notallowed

**Returns**:

()

**Remark:**

Deleting rows involves changing ordinal numbers of other rows remaining in the problem object. New ordinal numbers of the remaining rows are assigned under the assumption that the original order of rows is not changed.

**Example**:

```
> glp::del_rows lp [3, 4, 7];
()
```

**Synopsis**:

```
glp::del_cols lp cols
```

**Parameters**:

lp: pointer to the LP problem object cols: list of indices of columns to be deleted; the order of indices is not important, duplicates are notallowed

**Returns**:

()

**Remark:**

Deleting columns involves changing ordinal numbers of other columns remaining in the problem object. New ordinal numbers of the remaining columns are assigned under the assumption that the original order of columns is not changed.

**Example**:

```
> glp::del_cols lp [6, 4, 5];
()
```

**Synopsis**:

```
glp::copy_prob destination source names
```

**Parameters**:

destination: pointer to the destination LP problem object (must already exist)

source: pointer to the source LP problem object

names: one of the following:

glp::on: copy all symbolic names as well glp::off: do not copy the symbolic names

**Returns**:

()

**Example**:

```
> glp::copy_prob lp_dest lp_src glp::on;
()
```

**Synopsis**:

```
glp::erase_prob lp
```

**Parameters**:

lp: pointer to the LP problem object, it remains still valid after the function call

**Returns**:

()

**Example**:

```
> glp::erase_prob lp;
()
```

**Synopsis**:

```
glp::delete_prob lp
```

**Parameters**:

lp: pointer to the LP problem object, it is not valid any more after the function call

**Returns**:

()

**Example**:

```
> glp::delete_prob lp;
()
```

**Synopsis**:

```
glp::get_prob_name lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

name of the problem

**Example**:

```
> glp::get_prob_name lp;
"Testing problem"
```

**Synopsis**:

```
glp::get_obj_name lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

name of the objective

**Example**:

```
> glp::get_obj_name lp;
"Total costs"
```

**Synopsis**:

```
glp::get_obj_dir lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

returns one of the following:

glp::min: minimize glp::max: maximize

**Example**:

```
> glp::get_obj_dir lp;
glp::min
```

**Synopsis**:

```
glp::get_num_rows lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

number of rows (constraints)

**Example**:

```
> glp::get_num_rows lp;
58
```

**Synopsis**:

```
glp::get_num_cols lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

number of columns (structural variables)

**Example**:

```
> glp::get_num_cols lp;
65
```

**Synopsis**:

```
glp::get_row_name lp rowindex
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

name of the given row

**Example**:

```
> glp::get_row_name lp 3;
"The third row"
```

**Synopsis**:

```
glp::get_col_name lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

name of the given column

**Example**:

```
> glp::get_col_name lp 2;
"The second column"
```

**Synopsis**:

```
glp::get_row_type lp rowindex
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

returns one of the following:

glp::fr: free variable glp::lo: variable with lower bound glp::up: variable with upper bound glp::db: double bounded variable glp::fx: fixed variable

**Example**:

```
> glp::get_row_type lp 3;
glp::db
```

**Synopsis**:

```
glp::get_row_lb lp rowindex
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

the row lower bound; if the row has no lower bound then it returns the smallest double number

**Example**:

```
> glp::get_row_lb lp 3;
50.0
```

**Synopsis**:

```
glp::get_row_ub lp rowindex
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

the row upper bound; if the row has no upper bound then it returns the biggest double number

**Example**:

```
> glp::get_row_ub lp 3;
150.0
```

**Synopsis**:

```
glp::get_col_type lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

returns one of the following:

glp::fr: free variable glp::lo: variable with lower bound glp::up: variable with upper bound glp::db: double bounded variable glp::fx: fixed variable

**Example**:

```
> glp::get_col_type lp 2;
glp::up
```

**Synopsis**:

```
glp::get_col_lb lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

the column lower bound; if the column has no lower bound then it returns the smallest double number

**Example**:

```
> glp::get_col_lb lp 3;
-1.79769313486232e+308
```

**Synopsis**:

```
glp::get_col_ub lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

the column upper bound; if the column has no upper bound then it returns the biggest double number

**Example**:

```
> glp::get_col_lb lp 3;
150.0
```

**Synopsis**:

```
glp::get_obj_coef lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index; zero index denotes the constant term (objective shift)

**Returns**:

the coefficient of given column in the objective

**Example**:

```
> glp::get_obj_coef lp 3;
5.8
```

**Synopsis**:

```
glp::get_num_nz lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

number of non-zero coefficients in the problem matrix

**Example**:

```
> glp::get_num_nz lp;
158
```

**Synopsis**:

```
glp::get_mat_row lp rowindex
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

non-zero coefficients of the given row in a list form of tuples (colindex, coefficient)

**Example**:

```
> get_mat_row lp 3;
[(3,6.0),(2,2.0),(1,2.0)]
```

**Synopsis**:

```
glp::get_mat_col lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

non-zero coefficients of the given column in a list form of tuples (rowindex, coefficient)

**Example**:

```
> get_mat_col lp 2;
[(3,2.0),(2,4.0),(1,1.0)]
```

**Synopsis**:

```
glp::create_index lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

()

**Example**:

```
> glp::create_index lp;
()
```

**Synopsis**:

```
glp::find_row lp rowname
```

**Parameters**:

lp: pointer to the LP problem object rowname: row name

**Returns**:

ordinal number (index) of the row

**Remark**:

The search index is automatically created if it does not already exists.

**Example**:

```
> glp::find_row lp "The third row";
3
```

**Synopsis**:

```
glp::find_col lp colname
```

**Parameters**:

lp: pointer to the LP problem object colname: column name

**Returns**:

ordinal number (index) of the column

**Remark**:

The search index is automatically created if it does not already exists.

**Example**:

```
> glp::find_col lp "The second row";
2
```

**Synopsis**:

```
glp::delete_index lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

()

**Example**:

```
> glp::delete:index lp;
()
```

**Synopsis**:

```
glp::set_rii lp (rowindex, coefficient)
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index coefficient: scaling coefficient

**Returns**:

()

**Example**:

```
> glp::set_rii lp (3, 258.6);
()
```

**Synopsis**:

```
glp::set_sjj lp (colindex, coefficient)
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index coefficient: scaling coefficient

**Returns**:

()

**Example**:

```
> glp::set_sjj lp (2, 12.8);
()
```

**Synopsis**:

```
glp::get_rii lp rowindex
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

scaling coefficient of given row

**Example**:

```
> glp::get_rii lp 3;
258.6
```

**Synopsis**:

```
glp::get_sjj lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

scaling coefficient of given column

**Example**:

```
> glp::get_sjj lp 2;
12.8
```

**Synopsis**:

```
glp::scale_prob lp flags
```

**Parameters**:

lp: pointer to the LP problem object

flags: symbolic integer constants which can be combined together by arithmetic

or; the possible constants are:

glp::sf_gm: perform geometric mean scaling glp::sf_eq: perform equilibration scaling glp::sf_2n: round scale factors to power of two glp::sf_skip: skip if problem is well scaled glp::sf_auto: choose scaling options automatically

**Returns**:

()

**Example**:

```
> glp::scale_prob lp (glp::sf_gm || glp::sf_2n);
()
```

**Synopsis**:

```
glp::unscale_prob lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

()

**Example**:

```
> glp::unscale_prob lp;
()
```

**Synopsis**:

```
glp::set_row_stat lp (rowindex, status)
```

**Parameters**:

lp: pointer to the LP problem object

rowindex: row index

status: one of the following:

glp::bs: make the row basic (make the constraint inactive) glp::nl: make the row non-basic (make the constraint active) glp::nu: make the row non-basic and set it to the upper bound; if the row is not double-bounded, this status is equivalent to glp::nl (only in the case of this routine) glp::nf: the same as glp::nl (only in the case of this routine) glp::ns: the same as glp::nl (only in the case of this routine)

**Returns**:

()

**Example**:

```
> glp::set_row_stat lp (3, glp::nu);
()
```

**Synopsis**:

```
glp::set_col_stat lp (colindex, status)
```

**Parameters**:

lp: pointer to the LP problem object

colindex: column index

status: one of the following:

glp::bs: make the column basic glp::nl: make the column non-basic glp::nu: make the column non-basic and set it to the upper bound; if the column is not double-bounded, this status is equivalent to glp::nl (only in the case of this routine) glp::nf: the same as glp::nl (only in the case of this routine) glp::ns: the same as glp::nl (only in the case of this routine)

**Returns**:

()

**Example**:

```
> glp::set_col_stat lp (2, glp::bs);
()
```

**Synopsis**:

```
glp::std_basis lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

()

**Example**:

```
> glp::std_basis lp;
()
```

**Synopsis**:

```
glp::adv_basis lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

()

**Example**:

```
> glp::adv_basis lp;
()
```

**Synopsis**:

```
glp::cpx_basis lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

()

**Example**:

```
> glp::cpx_basis lp;
()
```

**Synopsis**:

```
glp::simplex lp options
```

**Parameters**:

lp: pointer to the LP problem object

options: list of solver options in the form of tuples (option_name, value):

glp::msg_lev:

- (default: glp::msg_all) - message level for
terminal output:

glp::msg_off:no outputglp::msg_err:error and warning messages onlyglp::msg_on:normal output;glp::msg_all:full output (including informational messages)glp::meth: (default: glp::primal) - simplex method option

glp::primal:use two-phase primal simplexglp::dual:use two-phase dual simplex;glp::dualp:use two-phase dual simplex, and if it fails, switch to the primal simplexglp::pricing: (default: glp::pt_pse) - pricing technique

glp::pt_std:standard (textbook)glp::pt_pse:projected steepest edgeglp::r_test: (default: glp::rt_har) - ratio test technique

glp::rt_std:standard (textbook)glp::rt_har:Harris’ two-pass ratio testglp::tol_bnd: (default: 1e-7) - tolerance used to check if the basic solution is primal feasible

glp::tol_dj: (default: 1e-7) - tolerance used to check if the basic solution is dual feasible

glp::tol_piv: (default: 1e-10) - tolerance used to choose eligble pivotal elements of the simplex table

glp::obj_ll: (default: -DBL_MAX) - lower limit of the objective function - if the objective function reaches this limit and continues decreasing, the solver terminates the search - used in the dual simplex only

glp::obj_ul: (default: +DBL_MAX) - upper limit of the objective function. If the objective function reaches this limit and continues increasing, the solver terminates the search - used in the dual simplex only

glp::it_lim: (default: INT_MAX) - simplex iteration limit

glp::tm lim: (default: INT_MAX) - searching time limit, in milliseconds

glp::out_frq: (default: 200) - output frequency, in iterations - this parameter specifies how frequently the solver sends information about the solution process to the terminal

glp::out_dly: (default: 0) - output delay, in milliseconds - this parameter specifies how long the solver should delay sending information about the solution process to the terminal

glp::presolve: (default: glp::off) - LP presolver option:

glp::on:enable using the LP presolverglp::off:disable using the LP presolver

**Returns**:

one of the following:

glp::ok: the LP problem instance has been successfully solved; this code does not necessarily mean that the solver has found optimal solution, it only means that the solution process was successful glp::ebadb: unable to start the search, because the initial basis specified in the problem object is invalid - the number of basic (auxiliary and structural) variables is not the same as the number of rows in the problem object glp::esing: unable to start the search, because the basis matrix corresponding to the initial basis is singular within the working precision glp::econd: unable to start the search, because the basis matrix corresponding to the initial basis is ill-conditioned, i.e. its condition number is too large glp::ebound: unable to start the search, because some double-bounded (auxiliary or structural) variables have incorrect bounds glp::efail: the search was prematurely terminated due to the solver failure glp::eobjll: the search was prematurely terminated, because the objective function being maximized has reached its lower limit and continues decreasing (the dual simplex only) glp::eobjul: the search was prematurely terminated, because the objective function being minimized has reached its upper limit and continues increasing (the dual simplex only) glp::eitlim: the search was prematurely terminated, because the simplex iteration limit has been exceeded glp::etmlim: the search was prematurely terminated, because the time limit has been exceeded glp::enopfs: the LP problem instance has no primal feasible solution (only if the LP presolver is used) glp::enodfs: the LP problem instance has no dual feasible solution (only if the LP presolver is used) When the list of options contains some bad option(s) then a list of bad options is returned instead.

**Remark**:

Options not mentioned in the option list are set to their default values.

**Example**:

```
> glp::simplex lp [(glp::presolve, glp::on), (glp::msg_lev, glp::msg_all)];
glp_simplex: original LP has 3 rows, 3 columns, 9 non-zeros
glp_simplex: presolved LP has 3 rows, 3 columns, 9 non-zeros
Scaling...
A: min|aij| = 1,000e+000 max|aij| = 1,000e+001 ratio = 1,000e+001
Problem data seem to be well scaled
Crashing...
Size of triangular part = 3
* 0: obj = 0,000000000e+000 infeas = 0,000e+000 (0)
* 2: obj = 7,333333333e+002 infeas = 0,000e+000 (0)
OPTIMAL SOLUTION FOUND
glp::ok
```

**Synopsis**:

```
glp::exact lp options
```

**Parameters**:

lp: pointer to the LP problem object

options: list of solver options in the form of tuples (option_name, value):

glp::it_lim: (default: INT_MAX) - simplex iteration limit glp::tm lim: (default: INT_MAX) - searching time limit, in milliseconds

**Returns**:

one of the following:

glp::ok: the LP problem instance has been successfully solved; this code does not necessarily mean that the solver has found optimal solution, it only means that the solution process was successful glp::ebadb: unable to start the search, because the initial basis specified in the problem object is invalid - the number of basic (auxiliary and structural) variables is not the same as the number of rows in the problem object glp::esing: unable to start the search, because the basis matrix corresponding to the initial basis is singular within the working precision glp::ebound: unable to start the search, because some double-bounded (auxiliary or structural) variables have incorrect bounds glp::efail: the search was prematurely terminated due to the solver failure glp::eitlim: the search was prematurely terminated, because the simplex iteration limit has been exceeded glp::etmlim: the search was prematurely terminated, because the time limit has been exceeded When the list of options contains some bad option(s) then a list of bad options is returned instead.

**Remark**:

Options not mentioned in the option list are set to their default values.

**Example**:

```
> glp::exact lp [];
glp_exact: 3 rows, 3 columns, 9 non-zeros
GNU MP bignum library is being used
* 2: objval = 0 (0)
* 4: objval = 733,333333333333 (0)
OPTIMAL SOLUTION FOUND
glp::ok
```

**Synopsis**:

```
glp::get_status lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

one of the following:

glp::undef: solution is undefined glp::feas: solution is feasible glp::infeas: solution is infeasible glp::nofeas: no feasible solution exists glp::opt: solution is optimal glp::unbnd: solution is unbounded

**Example**:

```
> glp::get_status lp;
glp::opt
```

**Synopsis**:

```
glp::get_prim_stat lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

one of the following:

glp::undef: primal solution is undefined glp::feas: primal solution is feasible glp::infeas: primal solution is infeasible glp::nofeas: no primal feasible solution exists

**Example**:

```
> glp::get_prim_stat lp;
glp::feas
```

**Synopsis**:

```
glp::get_dual_stat lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

one of the following:

glp::undef: dual solution is undefined glp::feas: dual solution is feasible glp::infeas: dual solution is infeasible glp::nofeas: no dual feasible solution exists

**Example**:

```
> glp::get_dual_stat lp;
glp::feas
```

**Synopsis**:

```
glp::get_obj_val lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

value of the objective function

**Example**:

```
> glp::get_obj_val lp
733.333333333333
```

**Synopsis**:

```
glp::get_row_stat lp rowindex
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

one of the following:

glp::bs: basic variable glp::nl: non-basic variable on its lower bound glp::nu: non-basic variable on its upper bound glp::nf: non-basic free (unbounded) variable glp::ns: non-basic fixed variable

**Example**:

```
> glp::get_row_stat lp 3;
glp::bs
```

**Synopsis**::- glp::get_row_prim lp rowindex

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

primal value of the row (auxiliary) variable

**Example**:

```
> glp::get_row_prim lp 3;
200.0
```

**Synopsis**:

```
glp::get_row_dual lp rowindex
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

dual value of the row (auxiliary) variable

**Example**:

```
> glp::get_row_dual lp 3;
0.0
```

**Synopsis**:

```
glp::get_col_stat lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

one of the following:

glp::bs: basic variable glp::nl: non-basic variable on its lower bound glp::nu: non-basic variable on its upper bound glp::nf: non-basic free (unbounded) variable glp::ns: non-basic fixed variable

**Example**:

```
> glp::get_col_stat lp 2;
glp::bs
```

**Synopsis**:

```
glp::get_col_prim lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

primal value of the column (structural) variable

**Example**:

```
> glp::get_col_prim lp 2;
66.6666666666667
```

**Synopsis**:

```
glp::get_col_dual lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

dual value of the column (structural) variable

**Example**:

```
> glp::get_col_dual lp 2;
0.0
```

**Synopsis**:

```
glp::get_unbnd_ray lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

The routine glp_get_unbnd_ray returns the number k of a variable, which causes primal or dual unboundedness. If 1 <= k <= m, it is k-th auxiliary variable, and if m + 1 <= k <= m + n, it is (k - m)-th structural variable, where m is the number of rows, n is the number of columns in the problem object. If such variable is not defined, the routine returns 0.

**Remark**:

If it is not exactly known which version of the simplex solver detected unboundedness, i.e. whether the unboundedness is primal or dual, it is sufficient to check the status of the variable with the routine glp::get_row_stat or glp::get_col_stat. If the variable is non-basic, the unboundedness is primal, otherwise, if the variable is basic, the unboundedness is dual (the latter case means that the problem has no primal feasible dolution).

**Example**:

```
> glp::get_unbnd_ray lp;
0
```

**Synopsis**:

```
glp::interior lp options
```

**Parameters**:

lp: pointer to the LP problem object

options: list of solver options in the form of tuples (option_name, value):

glp::msg_lev:

- (default: glp::msg_all) - message level for
terminal output:

glp::msg_off:no outputglp::msg_err:error and warning messages onlyglp::msg_on:normal output;glp::msg_all:full output (including informational messages)glp::ord_alg: (default: glp::ord_amd) - ordering algorithm option

glp::ord_none:use natural (original) orderingglp::ord_qmd:quotient minimum degree (QMD)glp::ord_amd:approximate minimum degree (AMD)glp::ord_sysamd:approximate minimum degree (SYSAMD)

**Returns**:

one of the following:

glp::ok: the LP problem instance has been successfully solved; this code does not necessarily mean that the solver has found optimal solution, it only means that the solution process was successful glp::efail: the problem has no rows/columns glp::enocvg: very slow convergence or divergence glp::eitlim: iteration limit exceeded glp::einstab: numerical instability on solving Newtonian system

**Example**:

```
> glp::interior lp [(glp::ord_alg, glp::ord_amd)];
Original LP has 3 row(s), 3 column(s), and 9 non-zero(s)
Working LP has 3 row(s), 6 column(s), and 12 non-zero(s)
Matrix A has 12 non-zeros
Matrix S = A*A' has 6 non-zeros (upper triangle)
Approximate minimum degree ordering (AMD)...
Computing Cholesky factorization S = L*L'...
Matrix L has 6 non-zeros
Guessing initial point...
Optimization begins...
0: obj = -8,218489503e+002; rpi = 3,6e-001; rdi = 6,8e-001; gap = 2,5e-001
1: obj = -6,719060895e+002; rpi = 3,6e-002; rdi = 1,9e-001; gap = 1,4e-002
2: obj = -6,917210389e+002; rpi = 3,6e-003; rdi = 9,3e-002; gap = 3,0e-002
3: obj = -7,267557732e+002; rpi = 2,1e-003; rdi = 9,3e-003; gap = 4,4e-002
4: obj = -7,323038146e+002; rpi = 2,1e-004; rdi = 1,1e-003; gap = 4,8e-003
5: obj = -7,332295932e+002; rpi = 2,1e-005; rdi = 1,1e-004; gap = 4,8e-004
6: obj = -7,333229585e+002; rpi = 2,1e-006; rdi = 1,1e-005; gap = 4,8e-005
7: obj = -7,333322959e+002; rpi = 2,1e-007; rdi = 1,1e-006; gap = 4,8e-006
8: obj = -7,333332296e+002; rpi = 2,1e-008; rdi = 1,1e-007; gap = 4,8e-007
9: obj = -7,333333230e+002; rpi = 2,1e-009; rdi = 1,1e-008; gap = 4,8e-008
10: obj = -7,333333323e+002; rpi = 2,1e-010; rdi = 1,1e-009; gap = 4,8e-009
OPTIMAL SOLUTION FOUND
glp::ok
```

**Synopsis**:

```
glp::ipt_status lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

one of the following

glp::undef: interior-point solution is undefined glp::opt: interior-point solution is optimal glp::infeas: interior-point solution is infeasible glp::nofeas: no feasible primal-dual solution exists

**Example**:

```
> glp::ipt_status lp;
glp::opt
```

**Synopsis**:

```
glp::ipt_obj_val lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

objective function value of interior-point solution

**Example**:

```
> glp::ipt_obj_val lp;
733.333332295849
```

**Synopsis**:

```
glp::ipt_row_prim lp rowindex
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

primal value of the row (auxiliary) variable

**Example**:

```
> glp::ipt_row_prim lp 3;
200.000000920688
```

**Synopsis**:

```
glp::ipt_row_dual lp rowindex
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

dual value of the row (auxiliary) variable

**Example**:

```
> glp::ipt_row_dual lp 3;
2.50607466186742e-008
```

**Synopsis**:

```
glp::ipt_col_prim lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

primal value of the column (structural) variable

**Example**:

```
> glp::ipt_col_prim lp 2;
66.666666406779
```

**Synopsis**:

```
glp::ipt_col_dual lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

dual value of the column (structural) variable

**Example**:

```
> glp::ipt_col_dual lp 2;
2.00019467655466e-009
```

**Synopsis**:

```
glp::set_col_kind lp (colindex, colkind)
```

**Parameters**:

lp: pointer to the LP problem object

colindex: column index

colkind: column kind - one of the following:

glp::cv: continuous variable glp::iv: integer variable glp::bv: binary variable

**Returns**:

()

**Example**:

```
> glp::set_col_kind lp (1, glp::iv);
()
```

**Synopsis**:

```
glp::get_col_kind lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

one of the following:

glp::cv: continuous variable glp::iv: integer variable glp::bv: binary variable

**Example**:

```
> glp::get_col_kind lp 1;
glp::iv
```

**Synopsis**:

```
glp::get_num_int lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

number of integer columns (including binary columns)

**Example**:

```
> glp_get_num_int lp;
1
```

**Synopsis**:

```
glp::get_num_bin lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

number of binary columns

**Example**:

```
> glp::get_num_bin lp
0
```

**Synopsis**:

```
glp::intopt lp options
```

**Parameters**:

lp: pointer to the LP problem object

options: list of solver options in the form of tuples (option_name, value):

glp::msg_lev:

- (default: glp::msg_all) - message level for
terminal output:

glp::msg_off:no outputglp::msg_err:error and warning messages onlyglp::msg_on:normal output;glp::msg_all:full output (including informational messages)glp::br_tech: (default: glp::bt::blb) - branching technique

glp::br_ffv:first fractional variableglp::br_lfv:last fractional variableglp::br_mfv:most fractional variableglp::br_dth:heuristic by Driebeck and Tomlinglp::br_pch:hybrid pseudocost heuristicglp::bt_tech: (default: glp::pt_pse) - backtracking technique

glp::bt_dfs:depth first search;glp::bt_bfs:breadth first search;glp::bt_blb:best local bound;glp::bt_bph:best projection heuristic.glp::pp_tech: (default: glp::pp_all) - preprocessing technique

glp::pp_none:disable preprocessing;glp::pp_root:perform preprocessing only on the root levelglp::pp_all:perform preprocessing on all levelsglp::fp_heur: (default: glp::off) - feasibility pump heuristic:

glp::on:enable applying the feasibility pump heuristicglp::off:disable applying the feasibility pump heuristicglp::gmi_cuts:

- (default: glp::off) - Gomory’s mixed integer
cuts:

glp::on:enable generating Gomory’s cuts;glp::off:disable generating Gomory’s cuts.glp::mir_cuts:

- (default: glp::off) - mixed integer rounding
(MIR) cuts:

glp::on:enable generating MIR cuts;glp::off:disable generating MIR cuts.glp::cov_cuts: (default: glp::off) - mixed cover cuts:

glp::on:enable generating mixed cover cuts;glp::off:disable generating mixed cover cuts.glp::clq_cuts (default: glp::off) - clique cuts:

glp::on:enable generating clique cuts;glp::off:disable generating clique cuts.glp::tol_int: (default: 1e-5) - absolute tolerance used to check if optimal solution to the current LP relaxation is integer feasible

glp::tol_obj: (default: 1e-7) - relative tolerance used to check if the objective value in optimal solution to the current LP relaxation is not better than in the best known integer feasible solution

glp::mip_gap: (default: 0.0) - the relative mip gap tolerance; if the relative mip gap for currently known best integer feasible solution falls below this tolerance, the solver terminates the search - this allows obtainig suboptimal integer feasible solutions if solving the problem to optimality takes too long time

glp::tm lim: (default: INT_MAX) - searching time limit, in milliseconds

glp::out_frq: (default: 5000) - output frequency, in miliseconds - this parameter specifies how frequently the solver sends information about the solution process to the terminal

glp::out_dly: (default: 10000) - output delay, in milliseconds - this parameter specifies how long the solver should delay sending information about the solution of the current LP relaxation with the simplex method to the terminal

glp::cb_func:

- (default: glp::off) - specifies whether to use
the user-defined callback routine

glp::on:use user-defined callback function - the functionglp::mip_cb tree infomustbe defined by the userglp::off:do not use user-defined callback functionglp::cb_info: (default: NULL) - transit pointer passed to the routine

glp::mip_cb tree info(see above)glp::cb_size: (default: 0) - the number of extra (up to 256) bytes allocated for each node of the branch-and-bound tree to store application-specific data - on creating a node these bytes are initialized by binary zeros

glp::presolve: (default: glp::off) - LP presolver option:

glp::on:enable using the MIP presolverglp::off:disable using the MIP presolverglp::binarize:

- (default: glp::off) - binarization (used only if
the presolver is enabled):

glp::on:replace general integer variables by binary onesglp::off:do not use binarization

**Returns**:

one of the following:

glp::ok: the MIP problem instance has been successfully solved; this code does not necessarily mean that the solver has found optimal solution, it only means that the solution process was successful glp::ebound: unable to start the search, because some double-bounded (auxiliary or structural) variables have incorrect bounds or some integer variables have non-integer (fractional) bounds glp::eroot: unable to start the search, because optimal basis for initial LP relaxation is not provided - this code may appear only if the presolver is disabled glp::enopfs: unable to start the search, because LP relaxation of the MIP problem instance has no primal feasible solution - this code may appear only if the presolver is enabled glp::enodfs: unable to start the search, because LP relaxation of the MIP problem instance has no dual feasible solution; in other word, this code means that if the LP relaxation has at least one primal feasible solution, its optimal solution is unbounded, so if the MIP problem has at least one integer feasible solution, its (integer) optimal solution is also unbounded - this code may appear only if the presolver is enabled glp::efail: the search was prematurely terminated due to the solver failure glp::emipgap: the search was prematurely terminated, because the relative mip gap tolerance has been reached glp::etmlim: the search was prematurely terminated, because the time limit has been exceeded glp::estop: the search was prematurely terminated by application - this code may appear only if the advanced solver interface is used When the list of options contains some bad option(s) then a list of bad options is returned instead.

**Remark**:

Options not mentioned in the option list are set to their default values.

**Example**:

```
> glp::intopt lp [(glp::presolve, glp::on)];
ipp_basic_tech: 0 row(s) and 0 column(s) removed
ipp_reduce_bnds: 2 pass(es) made, 3 bound(s) reduced
ipp_basic_tech: 0 row(s) and 0 column(s) removed
ipp_reduce_coef: 1 pass(es) made, 0 coefficient(s) reduced
glp_intopt: presolved MIP has 3 rows, 3 columns, 9 non-zeros
glp_intopt: 3 integer columns, none of which are binary
Scaling...
A: min|aij| = 1,000e+00 max|aij| = 1,000e+01 ratio = 1,000e+01
Problem data seem to be well scaled
Crashing...
Size of triangular part = 3
Solving LP relaxation...
* 2: obj = 0,000000000e+00 infeas = 0,000e+00 (0)
* 5: obj = 7,333333333e+02 infeas = 0,000e+00 (0)
OPTIMAL SOLUTION FOUND
Integer optimization begins...
+ 5: mip = not found yet <= +inf (1; 0)
+ 6: >>>>> 7,320000000e+02 <= 7,320000000e+02 0.0% (2; 0)
+ 6: mip = 7,320000000e+02 <= tree is empty 0.0% (0; 3)
INTEGER OPTIMAL SOLUTION FOUND
glp::ok
```

**Synopsis**:

```
glp::mip_status lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

one of the following:

glp::undef: MIP solution is undefined glp::opt: MIP solution is integer optimal glp::feas: MIP solution is integer feasible, however, its optimality (or non-optimality) has not been proven, perhaps due to premature termination of the search glp::nofeas: problem has no integer feasible solution (proven by the solver)

**Example**:

```
> glp::mip_status lp;
glp::opt
```

**Synopsis**:

```
glp::mip_obj_val lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

objective function value of mip solution

**Example**:

```
> glp::mip_obj_val lp;
732.0
```

**Synopsis**:

```
glp::mip_row_val lp rowindex
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

row value (value of auxiliary variable)

**Example**:

```
> glp::mip_row_val lp 3;
200.0
```

**Synopsis**:

```
glp::mip_col_val lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

column value (value of structural variable)

**Example**:

```
> glp::mip_col_val lp 2;
67.0
```

**Synopsis**:

```
glp::check_kkt lp solution condition
```

**Parameters**:

lp: pointer to the LP problem object

solution: one of the following

glp::sol: check basic solution glp::ipt: check interior-point solution glp::mip: check mixed integer solution condition: one of the following

glp::kkt_pe: check primal equality constraints glp::kkt_pb: check primal bound constraints glp::kkt_de: check dual equality constraints (not available for MIP) glp::kkt_db: check dual bound constraints (not available for MIP)

**Returns**:

tuple with four members (ae_max, ae_ind, re_max, re_ind) where the variables indicate:

ae_max: largest absolute error ae_ind: number of row (kkt_pe), column (kkt_de), or variable (kkt_pb, kkt_db) with the largest absolute error re_max: largest relative error re_ind: number of row (kkt_pe), column (kkt_de), or variable (kkt_pb, kkt_db) with the largest relative error where the variable index is (1 <= k <= m) for auxiliary variable and (m+1 <= k <= m+n) for structural variable

**Example**:

```
> glp::check_kkt lp glp::sol glp::kkt_pe;
0.0,0,0.0,0
> glp::check_kkt lp glp::mip glp::kkt_pe;
2.23517417907715e-008,1,7.50126764193079e-016,34169
>
```

**Synopsis**:

```
glp::read_mps lp format filename
```

**Parameters**:

lp: pointer to the LP problem object

format: one of the following

glp::mps_deck: fixed (ancient) MPS file format glp::mps_file: free (modern) MPS file format filename: file name - if the file name ends with suffix

.gz, the file is assumed to be compressed, in which case the routine glp::read_mps decompresses it “on the fly”

**Returns**:

0if reading went OK; non-zero in case of an error

**Example**:

```
> glp::read_mps lp glp::mps_deck "examples/plan.mps";
Reading problem data from `examples/plan.mps'...
Problem PLAN
Objective R0000000
8 rows, 7 columns, 55 non-zeros
63 records were read
0
```

**Synopsis**:

```
glp::write_mps lp format filename
```

**Parameters**:

lp: pointer to the LP problem object

format: one of the following

glp::mps_deck: fixed (ancient) MPS file format glp::mps_file: free (modern) MPS file format filename: file name - if the file name ends with suffix

.gz, the file is assumed to be compressed, in which case the routine glp_write_mps performs automatic compression on writing it

**Returns**:

0if writing went OK; non-zero in case of an error

**Example**:

```
> glp::write_mps lp glp::mps_file "examples/plan1.mps";
Writing problem data to `examples/plan1.mps'...
63 records were written
0
```

**Synopsis**:

```
glp::read_lp lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name - if the file name ends with suffix .gz, the file is assumed to be compressed, in which case the routine glp::read_lp decompresses it “on the fly”

**Returns**:

0if writing went OK; non-zero in case of an error

**Example**:

```
> glp::read_lp lp "examples/plan.lp";
reading problem data from `examples/plan.lp'...
8 rows, 7 columns, 48 non-zeros
39 lines were read
0
```

**Synopsis**:

```
glp::write_lp lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name - if the file name ends with suffix .gz, the file is assumed to be compressed, in which case the routine glp::write_lp performs automatic compression on writing it

**Returns**:

0if writing went OK; non-zero in case of an error

**Example**:

```
> glp::write_lp lp "examples/plan1.lp";
writing problem data to `examples/plan1.lp'...
29 lines were written
0
```

**Synopsis**:

```
glp::read_prob lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name - if the file name ends with suffix .gz, the file is assumed to be compressed, in which case the routine glp::read_prob decompresses it “on the fly”

**Returns**:

0if writing went OK; non-zero in case of an error

**Example**:

```
> glp::read_prob lp "examples/plan.glpk";
reading problem data from `examples/plan.glpk'...
8 rows, 7 columns, 48 non-zeros
86 lines were read
0
```

**Synopsis**:

```
glp::write_prob lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name - if the file name ends with suffix .gz, the file is assumed to be compressed, in which case the routine glp::write_prob performs automatic compression on writing it

**Returns**:

0if writing went OK; non-zero in case of an error

**Example**:

```
> glp::write_prob lp "examples/plan1.glpk";
writing problem data to `examples/plan1.glpk'...
86 lines were written
0
```

**Synopsis**:

```
glp::mpl_alloc_wksp
```

**Parameters**:

none

**Returns**:

pointer to the MathProg translator object

**Example**:

```
> let mpt = glp::mpl_alloc_wksp;
> mpt;
#<pointer 0xa0d0180>
```

**Synopsis**:

```
glp::mpl_read_model tranobject filename skip
```

**Parameters**:

tranobject: pointer to the MathProg translator object filename: file name skip: if 0then the data section from the model file is read; if non-zero, the data section in the data model is skipped

**Returns**:

0if reading went OK; non-zero in case of an error

**Example**:

```
> mpl_read_model mpt "examples/sudoku.mod" 1;
Reading model section from examples/sudoku.mod...
examples/sudoku.mod:69: warning: data section ignored
69 lines were read
0
```

**Synopsis**:

```
glp::mpl_read_data tranobject filename
```

**Parameters**:

tranobject: pointer to the MathProg translator object filename: file name

**Returns**:

0if reading went OK; non-zero in case of an error

**Example**:

```
> glp::mpl_read_data mpt "examples/sudoku.dat";
Reading data section from examples/sudoku.dat...
16 lines were read
0
```

**Synopsis**:

```
glp::mpl_generate tranobject filename
```

**Parameters**:

tranobject: pointer to the MathProg translator object filename: file name

**Returns**:

0if generating went OK; non-zero in case of an error

**Example**:

```
> glp::mpl_generate mpt "examples/sudoku.lst";
Generating fa...
Generating fb...
Generating fc...
Generating fd...
Generating fe...
Model has been successfully generated
0
```

**Synopsis**:

```
glp::mpl_build_prob tranobject lp
```

**Parameters**:

tranobject: pointer to the MathProg translator object lp: pointer to the LP problem object

**Returns**:

()

**Example**:

```
> glp::mpl_build_prob mpt lp;
()
```

**Synopsis**:

```
glp::mpl_postsolve tran lp solution
```

**Parameters**:

tranobject: pointer to the MathProg translator object

lp: pointer to the LP problem object

solution: one of the following:

glp::sol: use the basic solution glp::ipt: use the interior-point solution glp::mip: use mixed integer solution

**Returns**:

0if postsolve went OK; non-zero in case of an error

**Example**:

```
> glp::mpl_postsolve mpt lp glp::sol;
Model has been successfully processed
0
```

**Synopsis**:

```
glp::mpl_free_wksp tranobject
```

**Parameters**:

tranobject: pointer to the MathProg translator object

**Returns**:

()

**Example**:

```
> glp::mpl_free_wksp mpt;
()
```

**Synopsis**:

```
glp::print_sol lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name

**Returns**:

0if writing went OK; non-zero in case of an error

**Example**:

```
> glp::print_sol lp "examples/test.txt";
Writing basic solution to `examples/test.txt'...
0
```

**Synopsis**:

```
glp::read_sol lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name

**Returns**:

0if reading went OK; non-zero in case of an error

**Example**:

```
> glp::read_sol lp "examples/test.txt";
Reading basic solution from `examples/test.txt'...
1235 lines were read
0
```

**Synopsis**:

```
glp::write_sol lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name

**Returns**:

0if writing went OK; non-zero in case of an error

**Example**:

```
> glp::write_sol lp "examples/test.txt";
Writing basic solution to `examples/test.txt'...
1235 lines were written
0
```

**Synopsis**:

```
glp::print_ranges lp indices filename
```

**Parameters**:

lp: pointer to the LP problem object indices: list indices k of of rows and columns to be included in the report. If 1 ≤ k ≤ m, the basic variable is k-th auxiliary variable, and if m + 1 ≤ k ≤ m + n, the non-basic variable is (k − m)-th structural variable, where m is the number of rows and n is the number of columns in the specified problem object. An empty lists means printing report for all rows and columns. filename: file name

**Returns**:

0: if the operation was successful non-zero: if the operation failed

**Example**:

```
> glp::print_ranges lp [] "sensitivity.rpt";
Write sensitivity analysis report to `sensitivity.rpt'...
0
```

**Synopsis**:

```
glp::print_ipt lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name

**Returns**:

0if writing went OK; non-zero in case of an error

**Example**:

```
> glp::print_ipt lp "examples/test.txt";
Writing interior-point solution to `examples/test.txt'...
0
```

**Synopsis**:

```
glp::read_ipt lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name

**Returns**:

0if reading went OK; non-zero in case of an error

**Example**:

```
> glp::read_ipt lp "examples/test.txt";
Reading interior-point solution from `examples/test.txt'...
1235 lines were read
0
```

**Synopsis**:

```
glp::write_ipt lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name

**Returns**:

0if writing went OK; non-zero in case of an error

**Example**:

```
> glp::write_ipt lp "examples/test.txt";
Writing interior-point solution to `examples/test.txt'...
1235 lines were written
0
```

**Synopsis**:

```
glp::print_mip lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name

**Returns**:

0if writing went OK; non-zero in case of an error

**Example**:

```
> glp::print_mip lp "examples/test.txt";
Writing MIP solution to `examples/test.txt'...
0
```

**Synopsis**:

```
glp::read_mip lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name

**Returns**:

0if reading went OK; non-zero in case of an error

**Example**:

```
> glp::read_mip lp "examples/test.txt";
Reading MIP solution from `examples/test.txt'...
1235 lines were read
0
```

**Synopsis**:

```
glp::write_mip lp filename
```

**Parameters**:

lp: pointer to the LP problem object filename: file name

**Returns**:

0if writing went OK; non-zero in case of an error

**Example**:

```
> glp::write_mip lp "examples/test.txt";
Writing MIP solution to `examples/test.txt'...
1235 lines were written
0
```

**Synopsis**:

```
glp::bf_exists lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

non-zero: the basis factorization exists and can be used for calculations 0: the basis factorization does not exist

**Example**:

```
> glp::bf:exists lp;
1
```

**Synopsis**:

```
glp::factorize lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

one of the following:

glp::ok: the basis factorization has been successfully computed glp::ebadb: the basis matrix is invalid, because the number of basic (auxiliary and structural) variables is not the same as the number of rows in the problem object glp::esing: the basis matrix is singular within the working precision glp::exond: the basis matrix is ill-conditioned, i.e. its condition number is too large

**Example**:

```
> glp::factorize lp;
glp::ok
```

**Synopsis**:

```
glp::bf_updated lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

0: if the basis factorization has been just computed from “scratch” non-zero: if the factorization has been updated at least once

**Example**:

```
> glp::bf_updated lp;
0
```

**Synopsis**:

```
glp::get_bfcp lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

complete list of options in a form of tuples (option_name, value):

glp::fact_type: basis factorization type:

glp::bf_ft: LU + Forrest–Tomlin update glp::bf_bg: LU + Schur complement + Bartels–Golub update glp::bf_gr: LU + Schur complement + Givens rotation update glp::lu_size: the initial size of the Sparse Vector Area, in non-zeros, used on computing LU-factorization of the basis matrix for the first time - if this parameter is set to 0, the initial SVA size is determined automatically

glp::piv_tol: threshold pivoting (Markowitz) tolerance, 0 < piv_tol < 1, used on computing LU-factorization of the basis matrix

glp::piv_lim: this parameter is used on computing LU-factorization of the basis matrix and specifies how many pivot candidates needs to be considered on choosing a pivot element, piv_lim ≥ 1

glp::suhl: this parameter is used on computing LU-factorization of the basis matrix

glp::on: enables applying the heuristic proposed by Uwe Suhl glp::off: disables this heuristic glp::eps_tol: epsilon tolerance, eps_tol ≥ 0, used on computing LU-factorization of the basis matrix

glp::max_gro: maximal growth of elements of factor U, max_gro ≥ 1, allowable on computing LU-factorization of the basis matrix

glp::nfs_max: maximal number of additional row-like factors (entries of the eta file), nfs_max ≥ 1, which can be added to LU-factorization of the basis matrix on updating it with the Forrest–Tomlin technique

glp::upd_tol: update tolerance, 0 < upd_tol < 1, used on updating LU-factorization of the basis matrix with the Forrest–Tomlin technique

glp::nrs_max: maximal number of additional rows and columns, nrs_max ≥ 1, which can be added to LU-factorization of the basis matrix on updating it with the Schur complement technique

glp::rs_size: the initial size of the Sparse Vector Area, in non-zeros, used to store non-zero elements of additional rows and columns introduced on updating LU-factorization of the basis matrix with the Schur complement technique - if this parameter is set to 0, the initial SVA size is determined automatically

**Example**:

```
> glp::get_bfcp lp;
[(glp::fact_type,glp::bf_ft),(glp::lu_size,0),(glp::piv_tol,0.1),
(glp::piv_lim,4),(glp::suhl,glp::on),(glp::eps_tol,1e-15),
(glp::max_gro,10000000000.0),(glp::nfs_max,50),(glp::upd_tol,1e-06),
(glp::nrs_max,50),(glp::rs_size,0)]
```

**Synopsis**:

```
glp::set_bfcp lp options
```

**Parameters**:

lp: pointer to the LP problem object

options: list of options in a form of tuples (option_name, value):

glp::fact_type: (default: glp::bf_ft) - basis factorization type:

glp::bf_ft: LU + Forrest–Tomlin update glp::bf_bg: LU + Schur complement + Bartels–Golub update glp::bf_gr: LU + Schur complement + Givens rotation update glp::lu_size: (default: 0) - the initial size of the Sparse Vector Area, in non-zeros, used on computing LU-factorization of the basis matrix for the first time - if this parameter is set to 0, the initial SVA size is determined automatically

glp::piv_tol: (default: 0.10) - threshold pivoting (Markowitz) tolerance, 0 < piv_tol < 1, used on computing LU-factorization of the basis matrix.

glp::piv_lim: (default: 4) - this parameter is used on computing LU-factorization of the basis matrix and specifies how many pivot candidates needs to be considered on choosing a pivot element, piv_lim ≥ 1

glp::suhl: (default: glp::on) - this parameter is used on computing LU-factorization of the basis matrix.

glp::on: enables applying the heuristic proposed by Uwe Suhl glp::off: disables this heuristic glp::eps_tol: (default: 1e-15) - epsilon tolerance, eps_tol ≥ 0, used on computing LU -factorization of the basis matrix.

glp::max_gro: (default: 1e+10) - maximal growth of elements of factor U, max_gro ≥ 1, allowable on computing LU-factorization of the basis matrix.

glp::nfs_max: (default: 50) - maximal number of additional row-like factors (entries of the eta file), nfs_max ≥ 1, which can be added to LU-factorization of the basis matrix on updating it with the Forrest–Tomlin technique.

glp::upd_tol: (default: 1e-6) - update tolerance, 0 < upd_tol < 1, used on updating LU -factorization of the basis matrix with the Forrest–Tomlin technique.

glp::nrs_max: (default: 50) - maximal number of additional rows and columns, nrs_max ≥ 1, which can be added to LU-factorization of the basis matrix on updating it with the Schur complement technique.

glp::rs_size: (default: 0) - the initial size of the Sparse Vector Area, in non-zeros, used to store non-zero elements of additional rows and columns introduced on updating LU-factorization of the basis matrix with the Schur complement technique - if this parameter is set to 0, the initial SVA size is determined automatically

**Remarks**:

Options not mentioned in the option list are left unchanged.

All options will be reset to their default values when an empty option list is supplied.

**Returns**:

()if all options are OK, otherwise returns a list of bad options

**Example**:

```
> glp_set_bfcp lp [(glp::fact_type, glp::bf_ft), (glp::piv_tol, 0.15)];
()
```

**Synopsis**:

```
glp::get_bhead lp k
```

**Parameters**:

lp: pointer to the LP problem object k: variable index in the basis matrix

**Returns**:

If basic variable (xB )k , 1 ≤ k ≤ m, is i-th auxiliary variable (1 ≤ i ≤ m), the routine returns i. Otherwise, if (xB )k is j-th structural variable (1 ≤ j ≤ n), the routine returns m+j. Here m is the number of rows and n is the number of columns in the problem object.

**Example**:

```
> glp::get_bhead lp 3;
5
```

**Synopsis**:

```
glp::get_row_bind lp rowindex
```

**Parameters**:

lp: pointer to the LP problem object rowindex: row index

**Returns**:

This routine returns the index k of basic variable (xB )k, 1 ≤ k ≤ m, which is i-th auxiliary variable (that is, the auxiliary variable corresponding to i-th row), 1 ≤ i ≤ m, in the current basis associated with the specified problem object, where m is the number of rows. However, if i-th auxiliary variable is non-basic, the routine returns zero.

**Example**:

```
> glp::get_row_bind lp 3;
1
```

**Synopsis**:

```
glp::get_col_bind lp colindex
```

**Parameters**:

lp: pointer to the LP problem object colindex: column index

**Returns**:

This routine returns the index k of basic variable (xB )k, 1 ≤ k ≤ m, which is j-th structural variable (that is, the structural variable corresponding to j-th column), 1 ≤ j ≤ n, in the current basis associated with the specified problem object, where m is the number of rows, n is the number of columns. However, if j-th structural variable is non-basic, the routine returns zero.

**Example**:

```
> glp::get_col_bind lp 2;
3
```

**Synopsis**:

```
glp::ftran lp vector
```

**Parameters**:

lp: pointer to the LP problem object vector: vector to be transformed - a dense vector in a form of a list of double numbers has to be supplied and the number of its members must exactly correspond to the number of LP problem constraints

**Returns**:

the transformed vector in the same format

**Example**:

```
> glp::ftran lp [1.5, 3.2, 4.8];
[1.8,0.466666666666667,-1.96666666666667]
```

**Synopsis**:

```
glp::btran lp vector
```

**Parameters**:

lp: pointer to the LP problem object vector: vector to be transformed - a dense vector in a form of a list of double numbers has to be supplied and the number of its members must exactly correspond to the number of LP problem constraints

**Returns**:

the transformed vector in the same format

**Example**:

```
> glp::btran lp [1.5, 3.2, 4.8];
[-8.86666666666667,0.266666666666667,1.5]
```

**Synopsis**:

```
glp::warm_up lp
```

**Parameters**:

lp: pointer to the LP problem object

**Returns**:

one of the following:

glp::ok: the LP basis has been successfully “warmed up” glp::ebadb: the LP basis is invalid, because the number of basic variables is not the same as the number of rows glp::esing: the basis matrix is singular within the working precision glp::econd: the basis matrix is ill-conditioned, i.e. its condition number is too large

**Example**:

```
> glp::warm_up lp;
glp::e_ok
```

**Synopsis**:

```
glp::eval_tab_row lp k
```

**Parameters**:

lp: pointer to the LP problem object k: variable index such that it corresponds to some basic variable: if 1 ≤ k ≤ m, the basic variable is k-th auxiliary variable, and if m + 1 ≤ k ≤ m + n, the basic variable is (k − m)-th structural variable, where m is the number of rows and n is the number of columns in the specified problem object (the basis factorization must exist)

**Returns**:

simplex tableau row in a sparse form as a list of tuples (index, value), where index has the same meaning as k in parameters

**Example**:

```
> glp::eval_tab_row lp 3;
[(1,2.0),(6,4.0)]
```

**Synopsis**:

```
glp::eval_tab_col lp k
```

**Parameters**:

lp: pointer to the LP problem object k: variable index such that it corresponds to some non-basic variable: if 1 ≤ k ≤ m, the non-basic variable is k-th auxiliary variable, and if m + 1 ≤ k ≤ m + n, the non-basic variable is (k − m)-th structural variable, where m is the number of rows and n is the number of columns in the specified problem object (the basis factorization must exist)

**Returns**:

simplex tableau column in a sparse form as a list of tuples (index, value), where index has the same meaning as k in parameters

**Example**:

```
> glp::eval_tab_col lp 1;
[(3,2.0),(4,-0.666666666666667),(5,1.66666666666667)]
```

**Synopsis**:

```
glp::transform_row lp rowvector
```

**Parameters**:

lp: pointer to the LP problem object rowvector: row vector to be transformed in a sparse form as a list of tuples (k, value): if 1 ≤ k ≤ m, the non-basic variable is k-th auxiliary variable, and if m + 1 ≤ k ≤ m + n, the non-basic variable is (k − m)-th structural variable, where m is the number of rows and n is the number of columns in the specified problem object (the basis factorization must exist)

**Returns**:

the transformed row in a sparse form as a list of tuples (index, value), where index has the same meaning as k in parameters

**Example**:

```
> glp::transform_row lp [(1, 3.0), (2, 3.5)];
[(1,3.83333333333333),(2,-0.0833333333333333),(6,-3.41666666666667)]
```

**Synopsis**:

```
glp::transform_col lp colvector
```

**Parameters**:

lp: pointer to the LP problem object colvector: column vector to be transformed in a sparse form as a list of tuples (k, value): if 1 ≤ k ≤ m, the non-basic variable is k-th auxiliary variable, and if m + 1 ≤ k ≤ m + n, the non-basic variable is (k − m)-th structural variable, where m is the number of rows and n is the number of columns in the specified problem object (the basis factorization must exist)

**Returns**:

the transformed column in a sparse form as a list of tuples (index, value), where index has the same meaning as k in parameters

**Example**:

```
> glp::transform_col lp [(2, 1.0), (3, 2.3)];
[(3,2.3),(4,-0.166666666666667),(5,0.166666666666667)]
```

**Synopsis**:

```
glp::prim_rtest lp colvector dir eps
```

**Parameters**:

lp: pointer to the LP problem object colvector: simplex tableau column in a sparse form as a list of tuples (k, value): if 1 ≤ k ≤ m, the basic variable is k-th auxiliary variable, and if m + 1 ≤ k ≤ m + n, the basic variable is (k − m)-th structural variable, where m is the number of rows and n is the number of columns in the specified problem object (the basis factorization must exist and the primal solution must be feasible) dir: specifies in which direction the variable y changes on entering the basis: +1 means increasing, −1 means decreasing eps: relative tolerance (small positive number) used to skip small values in the column

**Returns**:

The routine returns the index, piv, in the colvector corresponding to the pivot element chosen, 1 ≤ piv ≤ len. If the adjacent basic solution is primal unbounded, and therefore the choice cannot be made, the routine returns zero.

**Example**:

```
> glp::prim_rtest lp [(3, 2.5), (5, 7.0)] 1 1.0e-5;
3
```

**Synopsis**:

```
glp::dual_rtest lp rowvector dir eps
```

**Parameters**:

lp: pointer to the LP problem object rowvector: simplex tableau row in a sparse form as a list of tuples (k, value): if 1 ≤ k ≤ m, the non-basic variable is k-th auxiliary variable, and if m + 1 ≤ k ≤ m + n, the non-basic variable is (k − m)-th structural variable, where m is the number of rows and n is the number of columns in the specified problem object (the basis factorization must exist and the dual solution must be feasible) dir: specifies in which direction the variable y changes on leaving the basis: +1 means increasing, −1 means decreasing eps: relative tolerance (small positive number) used to skip small values in the row

**Returns**:

The routine returns the index, piv, in the rowvector corresponding to the pivot element chosen, 1 ≤ piv ≤ len. If the adjacent basic solution is dual unbounded, and therefore the choice cannot be made, the routine returns zero.

**Example**:

```
> glp::dual_rtest lp [(1, 1.5), (6, 4.0)] 1 1.0e-5;
6
```

**Synopsis**:

```
glp::analyze_bound lp k
```

**Parameters**:

lp: pointer to the LP problem object k: if 1 ≤ k ≤ m, the non-basic variable is k-th auxiliary variable, and if m + 1 ≤ k ≤ m + n, the non-basic variable is (k − m)-th structural variable, where m is the number of rows and n is the number of columns in the specified problem object (the basis factorization must exist and the solution must be optimal)

**Returns**:

The routine returns a tuple (limit1, var1, limit2 var2) where:

value1: the minimal value of the active bound, at which the basis still remains primal feasible and thus optimal. -DBL_MAX means that the active bound has no lower limit. var1: the ordinal number of an auxiliary (1 to m) or structural (m + 1 to m + n) basic variable, which reaches its bound first and thereby limits further decreasing the active bound being analyzed. If value1 = -DBL_MAX, var1 is set to 0. value2: the maximal value of the active bound, at which the basis still remains primal feasible and thus optimal. +DBL_MAX means that the active bound has no upper limit. var2: the ordinal number of an auxiliary (1 to m) or structural (m + 1 to m + n) basic variable, which reaches its bound first and thereby limits further increasing the active bound being analyzed. If value2 = +DBL_MAX, var2 is set to 0.

**Example**:

```
> analyze_bound lp 2;
1995.06864446899,12,2014.03478832467,4
```

**Synopsis**:

```
glp::analyze_coef lp k
```

**Parameters**:

lp: pointer to the LP problem object k: if 1 ≤ k ≤ m, the basic variable is k-th auxiliary variable, and if m + 1 ≤ k ≤ m + n, the non-basic variable is (k − m)-th structural variable, where m is the number of rows and n is the number of columns in the specified problem object (the basis factorization must exist and the solution must be optimal)

**Returns**:

The routine returns a tuple (coef1, var1, value1, coef2 var2, value2) where:

coef1: the minimal value of the objective coefficient, at which the basis still remains dual feasible and thus optimal. -DBL_MAX means that the objective coefficient has no lower limit. var1: is the ordinal number of an auxiliary (1 to m) or structural (m + 1 to m + n) non-basic variable, whose reduced cost reaches its zero bound first and thereby limits further decreasing the objective coefficient being analyzed. If coef1 = -DBL_MAX, var1 is set to 0. value1: value of the basic variable being analyzed in an adjacent basis, which is defined as follows. Let the objective coefficient reaches its minimal value (coef1) and continues decreasing. Then the reduced cost of the limiting non-basic variable (var1) becomes dual infeasible and the current basis becomes non-optimal that forces the limiting non-basic variable to enter the basis replacing there some basic variable that leaves the basis to keep primal feasibility. Should note that on determining the adjacent basis current bounds of the basic variable being analyzed are ignored as if it were free (unbounded) variable, so it cannot leave the basis. It may happen that no dual feasible adjacent basis exists, in which case value1 is set to -DBL_MAX or +DBL_MAX. coef2: the maximal value of the objective coefficient, at which the basis still remains dual feasible and thus optimal. +DBL_MAX means that the objective coefficient has no upper limit. var2: the ordinal number of an auxiliary (1 to m) or structural (m + 1 to m + n) non-basic variable, whose reduced cost reaches its zero bound first and thereby limits further increasing the objective coefficient being analyzed. If coef2 = +DBL_MAX, var2 is set to 0. value2: value of the basic variable being analyzed in an adjacent basis, which is defined exactly in the same way as value1 above with exception that now the objective coefficient is increasing.

**Example**:

```
> analyze_coef lp 1;
-1.0,3,306.771624713959,1.79769313486232e+308,0,296.216606498195
```

All branch-and-cut API routines are supposed to be called from the callback routine. They cannot be called directly.

**Synopsis**:

```
glp::ios_reason tree
```

**Parameters**:

tree: pointer to the branch-and-cut search tree

**Returns**:

one of the following:

glp::irowgen: request for row generation glp::ibingo: better integer solution found glp::iheur: request for heuristic solution glp::icutgen: request for cut generation glp::ibranch: request for branching glp::iselect: request for subproblem selection glp::iprepro: request for preprocessing

**Example**:

```
glp::ios:reason tree;
```

**Synopsis**:

```
glp::ios_get_prob tree
```

**Parameters**:

tree: pointer to the branch-and-cut search tree

**Returns**:

The routine returns a pointer to the problem object used by the MIP solver.

**Example**:

```
glp::ios_get_prob tree;
```

**Synopsis**:

```
glp::ios_row_attr tree rowindex
```

**Parameters**:

tree: pointer to the branch-and-cut search tree rowindex: row index

**Returns**:

The routine returns a tuple consisting of three values (level, origin, klass):

level: subproblem level at which the row was created

origin: the row origin flag - one of the following:

glp::rf_reg: regular constraint glp::rf_lazy: “lazy” constraint glp::rf_cut: cutting plane constraint klass: the row class descriptor, which is a number passed to the routine glp_ios_add_row as its third parameter - if the row is a cutting plane constraint generated by the solver, its class may be the following:

glp::rf_gmi: Gomory’s mixed integer cut glp::rf_mir: mixed integer rounding cut glp::rf_cov: mixed cover cut glp::rf_clq: clique cut

**Example**:

```
glp::ios_row_attr tree 3;
```

**Synopsis**:

```
glp::ios_mip_gap tree
```

**Parameters**:

tree: pointer to the branch-and-cut search tree

**Returns**:

The routine returns the relative MIP gap.

**Example**:

```
> glp::ios_mip_gap tree;
```

**Synopsis**:

```
glp::ios_node_data tree node
```

**Parameters**:

tree: pointer to the branch-and-cut search tree

**Returns**:

The routine glp_ios_node_data returns a pointer to the memory block for the specified subproblem. Note that if cb_size = 0 was specified in the call of theintoptfunction, the routine returns a null pointer.

**Example**:

```
> glp::ios_node_data tree 23;
```

**Synopsis**:

```
glp::ios_select_node tree node
```

**Parameters**:

tree: pointer to the branch-and-cut search tree node: reference number of the subproblem from which the search will continue

**Returns**:

()

**Example**:

```
> glp::ios_select_node tree 23;
```

**Synopsis**:

```
glp::ios_heur_sol tree colvector
```

**Parameters**:

tree: pointer to the branch-and-cut search tree colvector: solution found by a primal heuristic. Primal values of all variables (columns) found by the heuristic should be placed in the list, i. e. the list must contain n numbers where n is the number of columns in the original problem object. Note that the routine does not check primal feasibility of the solution provided.

**Returns**:

If the provided solution is accepted, the routine returns zero. Otherwise, if the provided solution is rejected, the routine returns non-zero.

**Example**:

```
> glp::ios_heur_sol tree [15.7, (-3.1), 2.2];
```

**Synopsis**:

```
glp::ios_can_branch tree j
```

**Parameters**:

tree: pointer to the branch-and-cut search tree j: variable (column) index

**Returns**:

The function returns non-zero if j-th variable can be used for branching. Otherwise, it returns zero.

**Example**:

```
> glp::ios_can_branch tree 23;
```

**Synopsis**:

```
glp::ios_branch_upon tree j selection
```

**Parameters**:

tree: pointer to the branch-and-cut search tree

j: ordinal number of the selected branching variable

selection: one of the following:

glp::dn_brnch: select down-branch glp::up_brnch: select up-branch glp::no_brnch: use general selection technique

**Returns**:

()

**Example**:

```
> glp::ios_branch_upon tree 23 glp::up_brnch;
```

**Synopsis**:

```
glp::ios_terminate tree
```

**Parameters**:

tree: pointer to the branch-and-cut search tree

**Returns**:

()

**Example**:

```
> glp::ios_terminate tree;
```

**Synopsis**:

```
glp::ios_tree_size tree
```

**Parameters**:

tree: pointer to the branch-and-cut search tree

**Returns**:

The routine returns a tuple (a_cnt, n_cnt, t_cnt), where

a_cnt: the current number of active nodes n_cnt: the current number of all (active and inactive) nodes t_cnt: the total number of nodes including those which have been already removed from the tree. This count is increased whenever a new node appears in the tree and never decreased.

**Example**:

```
> glp::ios_tree_size tree;
```

**Synopsis**:

```
glp::ios_curr_node tree
```

**Parameters**:

tree: pointer to the branch-and-cut search tree

**Returns**:

The routine returns the reference number of the current active subproblem. If the current subproblem does not exist, the routine returns zero.

**Example**:

```
> glp::ios_curr_node tree;
```

**Synopsis**:

```
glp::ios_next_node tree node
```

**Parameters**:

tree: pointer to the branch-and-cut search tree node: reference number of an active subproblem or zero

**Returns**:

If the parameter p is zero, the routine returns the reference number of the first active subproblem. If the tree is empty, zero is returned. If the parameter p is not zero, it must specify the reference number of some active subproblem, in which case the routine returns the reference number of the next active subproblem. If there is no next active subproblem in the list, zero is returned. All subproblems in the active list are ordered chronologically, i.e. subproblem A precedes subproblem B if A was created before B.

**Example**:

```
> glp::ios_next_node tree 23;
```

**Synopsis**:

```
glp::ios_prev_node tree node
```

**Parameters**:

tree: pointer to the branch-and-cut search tree node: reference number of an active subproblem or zero

**Returns**:

If the parameter p is zero, the routine returns the reference number of the last active subproblem. If the tree is empty, zero is returned. If the parameter p is not zero, it must specify the reference number of some active subproblem, in which case the routine returns the reference number of the previous active subproblem. If there is no previous active subproblem in the list, zero is returned. All subproblems in the active list are ordered chronologically, i.e. subproblem A precedes subproblem B if A was created before B.

**Example**:

```
> glp::ios_prev_node tree 23;
```

**Synopsis**:

```
glp::ios_up_node tree node
```

**Parameters**:

tree: pointer to the branch-and-cut search tree node: reference number of an active or inactive subproblem

**Returns**:

The routine returns the reference number of its parent subproblem. If the specified subproblem is the root of the tree, the routine returns zero.

**Example**:

```
> glp::ios_up_node tree 23;
```

**Synopsis**:

```
glp::ios_node_level tree node
```

**Parameters**:

tree: pointer to the branch-and-cut search tree node: reference number of an active or inactive subproblem

**Returns**:

The routine returns the level of the given subproblem in the branch-and-bound tree. (The root subproblem has level 0.)

**Example**:

```
> glp::ios_node_level tree 23;
```

**Synopsis**:

```
glp::ios_node_bound tree node
```

**Parameters**:

tree: pointer to the branch-and-cut search tree node: reference number of an active or inactive subproblem

**Returns**:

The routine returns the local bound for the given subproblem.

**Example**:

```
> glp::ios_node_bound tree 23;
```

**Synopsis**:

```
glp::ios_best_node tree
```

**Parameters**:

tree: pointer to the branch-and-cut search tree

**Returns**:

The routine returns the reference number of the active subproblem, whose local bound is best (i.e. smallest in case of minimization or largest in case of maximization). If the tree is empty, the routine returns zero.

**Example**:

```
> glp::ios_best_node tree;
```

**Synopsis**:

```
glp::ios_pool_size tree
```

**Parameters**:

tree: pointer to the branch-and-cut search tree

**Returns**:

The routine returns the current size of the cut pool, that is, the number of cutting plane constraints currently added to it.

**Example**:

```
> glp::ios_pool_size tree;
```

**Synopsis**:

```
glp::ios_add_row tree (name, klass, flags, row, rowtype, rhs)
```

**Parameters**:

tree: pointer to the branch-and-cut search tree

name: symbolic name of the constraint

klass: specifies the constraint class, which must be either zero or a number in the range from 101 to 200. The application may use this attribute to distinguish between cutting plane constraints of different classes.

flags: currently is not used and must be zero

row: list of pairs (colindex, coefficient)

rowtype: one of the following:

glp::lo: ∑(aj.xj) ≥ RHS constraint glp::up: ∑(aj.xj) ≤ RHS constraint rhs: right hand side of the constraint

**Returns**:

The routine returns the ordinal number of the cutting plane constraint added, which is the new size of the cut pool.

**Example**:

```
> glp::ios_add_row tree ("new_constraint", 101, 0,
[(3, 15.0), (4, 6.7), (8, 1.25)], glp::up, 152.7);
```

**Synopsis**:

```
glp::ios_del_row tree rowindex
```

**Parameters**:

tree: pointer to the branch-and-cut search tree rowindex: index of row to be deleted from the cut pool

**Returns**:

()

**Remark**:

Note that deleting a constraint from the cut pool leads to changing ordinal numbers of other constraints remaining in the pool. New ordinal numbers of the remaining constraints are assigned under assumption that the original order of constraints is not changed.

**Example**:

```
> glp::ios_del_row tree 5;
```

**Synopsis**:

```
glp::ios_clear_pool tree
```

**Parameters**:

tree: pointer to the branch-and-cut search tree

**Returns**:

()

**Example**:

```
> glp::ios_clear_pool tree;
```

**Synopsis**:

```
glp::create_graph v_size a_size
```

**Parameters**:

v_size: size of vertex data blocks, in bytes, 0 ≤ v size ≤ 256 a_size: size of arc data blocks, in bytes, 0 ≤ a size ≤ 256.

**Returns**:

The routine returns a pointer to the graph created.

**Example**:

```
> let g = glp::create_graph 32 64;
> g;
#<pointer 0x9de7168>
```

**Synopsis**:

```
glp::set_graph_name graph name
```

**Parameters**:

graph: pointer to the graph object name: the graph name, an empty string erases the current name

**Returns**:

()

**Example**:

```
> glp::set_graph_name graph "MyGraph";
()
```

**Synopsis**:

```
glp::add_vertices graph count
```

**Parameters**:

graph: pointer to the graph object count: number of vertices to add

**Returns**:

The routine returns the ordinal number of the first new vertex added to the graph.

**Example**:

```
> glp::add_vertices graph 5;
18
```

**Synopsis**:

```
glp::add_arc graph i j
```

**Parameters**:

graph: pointer to the graph object i: index of the tail vertex j: index of the head vertex

**Returns**:

()

**Example**:

```
> glp::add_arc graph 7 12;
()
```

**Synopsis**:

```
glp::erase_graph graph v_size a_size
```

**Parameters**:

graph: pointer to the graph object v_size: size of vertex data blocks, in bytes, 0 ≤ v size ≤ 256 a_size: size of arc data blocks, in bytes, 0 ≤ a size ≤ 256.

**Returns**:

()

**Remark**:

The routine reinitialises the graph object. Its efect is equivalent to calling delete_graph followed by a call to create_graph.

**Example**:

```
> glp::erase_graph graph 16 34;
()
```

**Synopsis**:

```
glp::delete_graph graph
```

**Parameters**:

graph: pointer to the graph object

**Returns**:

()

**Remark**:

The routine destroys the graph object and invalidates the pointer. This is done automatically when the graph is not needed anymore, the routine need not be usually called.

**Example**:

```
> glp::delete_graph graph
()
```

**Synopsis**:

```
glp::read_graph graph filename
```

**Parameters**:

graph: pointer to the graph object filename: file name

**Returns**:

0if reading went OK; non-zero in case of an error

**Example**:

```
> glp::read_graph graph "graph_data.txt";
0
```

**Synopsis**:

```
glp::write_graph graph filename
```

**Parameters**:

graph: pointer to the graph object filename: file name

**Returns**:

0if reading went OK; non-zero in case of an error

**Example**:

```
> glp::write_graph graph "graph_data.txt";
0
```

**Synopsis**:

```
glp::weak_comp graph v_num
```

**Parameters**:

graph: pointer to the graph object v_num: offset of the field of type int in the vertex data block, to which the routine stores the number of a weakly connected component containing that vertex - if v_num < 0, no component numbers are stored

**Returns**:

The routine returns the total number of components found.

**Example**:

```
> glp::weak_comp graph 16;
3
```

**Synopsis**:

```
glp::strong_comp graph v_num
```

**Parameters**:

graph: pointer to the graph object v_num: offset of the field of type int in the vertex data block, to which the routine stores the number of a strongly connected component containing that vertex - if v_num < 0, no component numbers are stored

**Returns**:

The routine returns the total number of components found.

**Example**:

```
> glp::strong_comp graph 16;
4
```

**Synopsis**:

```
glp::read_mincost graph v_rhs a_low a_cap a_cost filename
```

**Parameters**:

graph: pointer to the graph object v_rhs: offset of the field of type double in the vertex data block, to which the routine stores bi, the supply/demand value - if v_rhs < 0, the value is not stored a_low: offset of the field of type double in the arc data block, to which the routine stores lij, the lower bound to the arc flow - if a_low < 0, the lower bound is not stored a_cap: offset of the field of type double in the arc data block, to which the routine stores uij, the upper bound to the arc flow (the arc capacity) - if a_cap < 0, the upper bound is not stored a_cost: offset of the field of type double in the arc data block, to which the routine stores cij, the per-unit cost of the arc flow - if a_cost < 0, the cost is not stored fname: the name of a text file to be read in - if the file name name ends with the suffix ‘.gz’, the file is assumed to be compressed, in which case the routine decompresses it “on the fly”

**Returns**:

0if reading went OK; non-zero in case of an error

**Example**:

```
> glp::read_mincost graph 0 8 16 24 "graphdata.txt";
0
```

**Synopsis**:

```
glp::write_mincost graph v_rhs a_low a_cap a_cost fname
```

**Parameters**:

graph: pointer to the graph object v_rhs: offset of the field of type double in the vertex data block, to which the routine stores bi, the supply/demand value - if v_rhs < 0, the value is not stored a_low: offset of the field of type double in the arc data block, to which the routine stores lij, the lower bound to the arc flow - if a_low < 0, the lower bound is not stored a_cap: offset of the field of type double in the arc data block, to which the routine stores uij, the upper bound to the arc flow (the arc capacity) - if a_cap < 0, the upper bound is not stored a_cost: offset of the field of type double in the arc data block, to which the routine stores cij, the per-unit cost of the arc flow - if a_cost < 0, the cost is not stored fname: the name of a text file to be written out - if the file name name ends with the suffix ‘.gz’, the file is assumed to be compressed, in which case the routine compresses it “on the fly”

**Returns**:

0if reading went OK; non-zero in case of an error

**Example**:

```
> glp::write_mincost graph 0 8 16 24 "graphdata.txt";
0
```

**Synopsis**:

```
glp::mincost_lp lp graph names v_rhs a_low a_cap a_cost
```

**Parameters**:

lp: pointer to the LP problem object

graph: pointer to the graph object

names: one of the following:

glp::on: assign symbolic names of the graph object components to symbolic names of the LP problem object components glp::off: no symbolic names are assigned v_rhs: offset of the field of type double in the vertex data block, to which the routine stores bi, the supply/demand value - if v_rhs < 0, it is assumed bi = 0 for all nodes

a_low: offset of the field of type double in the arc data block, to which the routine stores lij, the lower bound to the arc flow - if a_low < 0, it is assumed lij = 0 for all arcs

a_cap: offset of the field of type double in the arc data block, to which the routine stores uij, the upper bound to the arc flow (the arc capacity) - if a_cap < 0,it is assumed uij = 1 for all arcs, value of DBL_MAX means an uncapacitated arc

a_cost: offset of the field of type double in the arc data block, to which the routine stores cij, the per-unit cost of the arc flow - if a_cost < 0, it is assumed cij = 0 for all arcs

**Returns**:

()

**Example**:

```
> glp::mincost_lp lp graph glp::on 0 8 16 24;
()
```

**Synopsis**:

```
glp::mincost_okalg graph v_rhs a_low a_cap a_cost a_x v_pi
```

**Parameters**:

graph: pointer to the graph object v_rhs: offset of the field of type double in the vertex data block, to which the routine stores bi, the supply/demand value - if v_rhs < 0, it is assumed bi = 0 for all nodes a_low: offset of the field of type double in the arc data block, to which the routine stores lij, the lower bound to the arc flow - if a_low < 0, it is assumed lij = 0 for all arcs a_cap: offset of the field of type double in the arc data block, to which the routine stores uij, the upper bound to the arc flow (the arc capacity) - if a_cap < 0,it is assumed uij = 1 for all arcs, value of DBL_MAX means an uncapacitated arc a_cost: offset of the field of type double in the arc data block, to which the routine stores cij, the per-unit cost of the arc flow - if a_cost < 0, it is assumed cij = 0 for all arcs a_x: offset of the field of type double in the arc data block, to which the routine stores xij, the arc flow found - if a_x < 0, the arc flow value is not stored v_pi: specifies an offset of the field of type double in the vertex data block, to which the routine stores pi, the node potential, which is the Lagrange multiplier for the corresponding flow conservation equality constraint

**Remark**:

Note that all solution components (the objective value, arc flows, and node potentials) computed by the routine are always integer-valued.

**Returns**:

The function returns a tuple in the form

(code, obj), wherecodeis one of the following

glp::ok: optimal solution found glp::enopfs: no (primal) feasible solution exists glp::edata: unable to start the search, because some problem data are either not integer-valued or out of range; this code is also returned if the total supply, which is the sum of bi over all source nodes (nodes with bi > 0), exceeds INT_MAX glp::erange: the search was prematurely terminated because of integer overflow glp::efail: an error has been detected in the program logic - if this code is returned for your problem instance, please report to <bug-glpk@gnu.org> and

objis value of the objective function.

**Example**:

```
> glp::mincost_okalg graph 0 8 16 24 32 40;
(glp::ok, 15)
```

**Synopsis**:

```
glp::netgen graph v_rhs a_cap a_cost parameters
```

**Parameters**:

graph: pointer to the graph object

v_rhs: offset of the field of type double in the vertex data block, to which the routine stores bi, the supply/demand value - if v_rhs < 0, it is assumed bi = 0 for all nodes

a_cap: offset of the field of type double in the arc data block, to which the routine stores uij, the upper bound to the arc flow (the arc capacity) - if a_cap < 0,it is assumed uij = 1 for all arcs, value of DBL_MAX means an uncapacitated arc

a_cost: offset of the field of type double in the arc data block, to which the routine stores cij, the per-unit cost of the arc flow - if a_cost < 0, it is assumed cij = 0 for all arcs

parameters: tuple of exactly 15 integer numbers with the following meaning:

parm[1]: iseed 8-digit positive random number seed parm[2]: nprob 8-digit problem id number parm[3]: nodes total number of nodes parm[4]: nsorc total number of source nodes (including transshipment nodes) parm[5]: nsink total number of sink nodes (including transshipment nodes) parm[6]: iarcs number of arc parm[7]: mincst minimum cost for arcs parm[8]: maxcst maximum cost for arcs parm[9]: itsup total supply parm[10]: ntsorc number of transshipment source nodes parm[11]: ntsink number of transshipment sink nodes parm[12]: iphic percentage of skeleton arcs to be given the maximum cost parm[13]: ipcap percentage of arcs to be capacitated parm[14]: mincap minimum upper bound for capacitated arcs parm[15]: maxcap maximum upper bound for capacitated arcs

**Returns**:

0if the instance was successfully generated, nonzero otherwise

**Example**:

```
> glp::netgen graph 0 8 16 (12345678, 87654321, 20, 12, 8,
25, 5, 20, 300, 6, 5, 15, 100, 1, 30);
0
```

**Synopsis**:

```
glp::gridgen graph v_rhs a_cap a_cost parameters
```

**Parameters**:

graph: pointer to the graph object

v_rhs: a_cap: a_cost: parameters: tuple of exactly 14 integer numbers with the following meaning:

parm[1]: two-ways arcs indicator:

1:if links in both direction should be generated0:otherwiseparm[2]: random number seed (a positive integer)

parm[3]: number of nodes (the number of nodes generated might be slightly different to make the network a grid)

parm[4]: grid width

parm[5]: number of sources

parm[6]: number of sinks

parm[7]: average degree

parm[8]: total flow

parm[9]: distribution of arc costs:

1:uniform2:exponentialparm[10]: lower bound for arc cost (uniform), 100 lambda¸ (exponential)

parm[11]: upper bound for arc cost (uniform), not used (exponential)

parm[12]: distribution of arc capacities:

1:uniform2:exponentialparm[13]: lower bound for arc capacity (uniform), 100 lambda (exponential)

parm[14]: upper bound for arc capacity (uniform), not used (exponential)

**Returns**:

0if the instance was successfully generated, nonzero otherwise

**Example**:

```
> glp::gridgen graph 0 8 16 (1, 123, 20, 4, 7, 5, 3, 300, 1, 1, 5, 1, 5, 30);
0
```

**Synopsis**:

```
glp::read_maxflow graph a_cap filename
```

**Parameters**:

graph: pointer to the graph object

**Returns**:

**Example**:

```
>
```

**Synopsis**:

```
glp::write_maxflow graph s t a_cap filename
```

**Parameters**:

graph: pointer to the graph object

**Returns**:

**Example**:

```
>
```

**Synopsis**:

```
glp::maxflow_lp lp graph names s t a_cap
```

**Parameters**:

graph: pointer to the graph object

**Returns**:

**Example**:

```
>
```

**Synopsis**:

```
glp::maxflow_ffalg graph s t a_cap a_x v_cut
```

**Parameters**:

graph: pointer to the graph object

**Returns**:

**Example**:

```
>
```

**Synopsis**:

```
glp::rmfgen graph a_cap parameters
```

**Parameters**:

graph: pointer to the graph object

**Returns**:

**Example**:

```
>
```

**Synopsis**:

```
`glp::version
```

**Parameters**:

none

**Returns**:

GLPK library version

**Example**:

```
> glp::version;
"4.38"
```

**Synopsis**:

```
glp::term_out switch
```

**Parameters**:

switch: one of the following:

glp::on: enable terminal output from GLPK routines glp::off: disable terminal output from GLPK routines

**Returns**:

()

**Example**:

```
> glp::term_out glp:off;
()
```

**Synopsis**:

```
glp::term_hook switch info
```

**Parameters**:

switch: one of the following:

glp::on: use the terminal callback function glp::off: don’t use the terminal callback function info: pointer to a memory block which can be used for passing additional information to the terminal callback function

**Returns**:

()

**Example**:

```
> glp::term_hook glp::on NULL;
()
```

**Synopsis**:

```
glp::mem_usage
```

**Parameters**:

none

**Returns**:

tuple consisting of four numbers:

count(int) - the number of currently allocated memory blockscpeak(int) - the peak value ofcountreached since the initialization of the GLPK library environmenttotal(bigint) - the total amount, in bytes, of currently allocated memory blockstpeak(bigint) - the peak value oftotalreached since the initialization of the GLPK library envirionment

**Example**:

```
> glp::mem_usage;
7,84,10172L,45304L
```

**Synopsis**:

```
glp::mem_limit limit
```

**Parameters**:

limit: memory limit in megabytes

**Returns**:

()

**Example**:

```
> glp::mem_limit 200;
()
```

**Synopsis**:

```
glp::free_env
```

**Parameters**:

none

**Returns**:

()

**Example**:

```
> glp_free_env;
()
```